RRKM dynamics

In the above discussion it was assumed that the barriers are low for transitions between the different confonnations of the fluxional molecule, as depicted in figure A3.12.5 and therefore the transitions occur on a timescale much shorter than the RRKM lifetime. This is the rapid IVR assumption of RRKM theory discussed in section A3.12.2. Accordingly, an initial microcanonical ensemble over all the confonnations decays exponentially. However, for some fluxional molecules, transitions between the different confonnations may be slower than the RRKM rate, giving rise to bottlenecks in the unimolecular dissociation [4, ]. The ensuing lifetime distribution, equation (A3.12.7), will be non-exponential, as is the case for intrinsic non-RRKM dynamics, for an mitial microcanonical ensemble of molecular states. 

The first classical trajectory study of iinimoleciilar decomposition and intramolecular motion for realistic anhannonic molecular Hamiltonians was perfonned by Bunker [12,13], Both intrinsic RRKM and non-RRKM dynamics was observed in these studies. Since this pioneering work, there have been numerous additional studies [9,k7,30,M,M, ai d from which two distinct types of intramolecular motion, chaotic and quasiperiodic [14], have been identified. Both are depicted in figure A3,12,7. Chaotic vibrational motion is not regular as predicted by tire nonnal-mode model and, instead, there is energy transfer between the modes. If all the modes of the molecule participate in the chaotic motion and energy flow is sufficiently rapid, an initial microcanonical ensemble is maintained as the molecule dissociates and RRKM behaviour is observed [9], For non-random excitation initial apparent non-RRKM behaviour is observed, but at longer times a microcanonical ensemble of states is fonned and the probability of decomposition becomes that of RRKM theory. 

Apparent non-RRKM behaviour occurs when the molecule is excited non-randomly and there is an initial non-RRKM decomposition before IVR fomis a microcanonical ensemble (see section A3.12.2). Reaction patliways, which have non-competitive RRKM rates, may be promoted in this way. Classical trajectory simulations were used in early studies of apparent non-RRKM dynamics [113.114]. 

Apparent non-RRKM dynamics has also been observed in time-resolved femtosecond (fs) experiments in a collision-free enviromnent [117], An experimental study of acetone illustrates this work. Acetone is dissociated to the CH and CH CO (acetyl) radicals by a fs laser pulse. The latter which dissociates by the channel... 

Definitive examples of intrinsic non-RRKM dynamics for molecules excited near their unimolecular tluesholds are rather limited. Calculations have shown that intrinsic non-RRKM dynamics becomes more pronounced at very high energies, where the RRKM lifetime becomes very short and dissociation begins to compete with IVR [119]. There is a need for establishing quantitative theories (i.e. not calculations) for identifying which molecules and energies lead to intrinsic non-RRKM dynamics. For example, at thenual... 

It should be pointed out that while most of the reactions can be solved using traditional RRKM approach, experimental and theoretical studies have shown that non-RRKM dynamics is important for moderate to large-sized molecules with various barriers for unimolecular dissociation [57,58]. In these cases, non-RRKM behavior needs to be taken into account and direct chemical dynamic simulation is suggested to serve this purpose [58]. 

It is not immediately obvious, by simply looking at a molecule s Hamiltonian and/or its PES, whether the unimolecular dynamics will be intrinsic RRKM or not and computer simulations as outlined here are required. Intrinsic non-RRKM dynamics is indicative of mode-specific decomposition, since different regions of phase space are not strongly coupled and a micro-canonical ensemble is not maintained during the fragmentation. The phase space structures, which give rise to intrinsic RRKM or non-RRKM behavior, are discussed in the next section. 

A classical diffusion theory model has been proposed to calculate the rate of IVR between the reaction coordinate and the remaining bath modes of the molecule [345]. Following work by Bunker [324], the unimolecular dynamics will be non-ergodic (intrinsically non-RRKM) if A rrkm fciVR. For such a situation, the unimolecular decomposition will be exponential and occur with a rate constant equal to /sivr- The rate of IVR is modeled by assuming a random force between the bath modes and the reaction coordinate. The model was used to successfully analyze the intrinsic non-RRKM dynamics for Si2He -> 2SiH3 dissociation [345]. 

If an intrinsically-RRKM molecule with many atoms is excited non-randomly, its initial classical non-RRKM dynamics may agree with the quantum dynamics for the reasons described above. But at longer times, after a micro-canonical ensemble is created, the classical unimolecular rate constant is much larger than the quantum value, because of the zero-point energy problem. Thus, the short-time unimolecular dynamics of a large molecule will often agree quite well with experiment if the molecule is excited non-randomly. The following is a brief review of two representative... 

This minimally dynamic approach has been applied to both bimolecular and unimolecular reactions a typical result for the latter case is shown in Fig. 6. In this case we consider the dissociation of CCH on two different potential surfaces due to Wolf and Hase.36 These authors classified the first surface (their case IIC) as yielding RRKM dissociation, whereas their surface IIA yielded non-RRKM dynamics. The exact trajectory results for translational, vibrational, and rotational distributions for these two cases are shown as solid histograms in Fig. 6. The minimally dynamic construction, which requires only short-lived trajectory calculations, are shown as dashed histograms in the same figure and are seen to be in excellent agreement with the exact results. 

Fig. 15.2. Trajectory lifetime distributions for HCO, HNO, and HO2 dissociation, following microcanonical sampling. Extensive intrinsic non-RRKM dynamics are present in HCO and HNO decomposition. The smooth curves are obtained by fitting the data to an exponential function, with the initial fast decomposition times being excluded. Adapted from Ref. [51].

Intrinsic RRKM behavior is defined by Eq. (3), where an initial microcanonical ensemble of states decomposes exponentially with the RRKM rate constant [56]. Such dynamics can be investigated by computational chemical dynamics simulations. Therefore, an intrinsic non-RRKM molecule is one for which the intercept in P(t) is k(E), as a result of the initial microcanonical ensemble, but whose decomposition probability versus time is not described by k E). For such a molecule there is a bottleneck (or bottlenecks) restricting energy flow into the dissociating coordinate. Intrinsic RRKM and non-RRKM dynamics are illustrated in Fig. 15.3(a), (b), and (e). 

Trajectory calculations have been used to study the intrinsic RRKM and apparent non-RRKM dynamics of ethyl radical dissociation, i.e. C2H5 — H - - C2H4 [61,62]. When C2H5 is excited randomly, with a microcanonical distribution of states, it dissociates with the exponential P t) of RRKM theory [61], i.e. it is an intrinsic RRKM molecule. However, apparent non-RRKM behavior is present in a trajectory simulation of C2H5... 

The above apparent non-RRKM and intrinsic RRKM and non-RRKM dynamics are reflections of a molecule s phase space structure. Extensive calculations and study of the classical dynamics of vibrationally excited molecules have shown that they may have different types of motions, e.g. regular and irregular [63]. A trajectory is regular if its motion may be represented by a separable Hamiltonian, for which each degree of freedom is uncoupled and moves independent of the other degrees of freedom. All trajectories are regular for the normal mode Hamiltonian, i.e. 

CU-CH3CI decomposition MP2/6-31G- [C1-CH3-C1] central barrier recrossing and intrinsic non-RRKM dynamics [121]... 

Cr (CO)6 and protonated peptide surface induced dissociation (SID) AMI Shattering fragmentation, apparent non-RRKM dynamics [123-125]... 

Vinylcyclopropane — cyclopentene rearrangement AMl-SRP Apparent non-RRKM dynamics [126,127]... 

See, for example, D. L. Bunker, /. Chem. Phys., 40,1946 (1963). Monte Carlo Calculations. IV. Further Studies of Unimolecular Dissociation. D. L. Bunker and M. Pattengill,/. Chem. Phys., 48, 772 (1968). Monte Carlo Calculations. VI. A Re-evaluation erf Ae RRKM Theory of Unimolecular Reaction Rates. W. J. Hase and R. J. Wolf, /. Chem. Phys., 75,3809 (1981). Trajectory Studies of Model HCCH H -P HCC Dissociation. 11. Angular Momenta and Energy Partitioning and the Relation to Non-RRKM Dynamics. D. W. Chandler, W. E. Farneth, and R. N. Zare, J. Chem. Phys., 77, 4447 (1982). A Search for Mode-Selective Chemistry The Unimolecular Dissociation of t-Butyl Hydroperoxide Induced by Vibrational Overtone Excitation. J. A. Syage, P. M. Felker, and A. H. Zewail, /. Chem. Phys., 81, 2233 (1984). Picosecond Dynamics and Photoisomerization of Stilbene in Supersonic Beams. II. Reaction Rates and Potential Energy Surface. D. B. Borchardt and S. H. Bauer, /. Chem. Phys., 85, 4980 (1986). Intramolecular Conversions Over Low Barriers. VII. The Aziridine Inversion—Intrinsically Non-RRKM. A. H. Zewail and R. B. Bernstein,... 

This work led to the understanding of intrinsic RRKM and non-RRKM dynamics for unimolecular reactions. ... 

This chapter includes a derivation of the expression of the RRKM unimolecular rate constant discussions of intrinsic RRKM and non-RRKM unimolecular dynamics, and how these dynamics are alfeeted by the classical phase space structure of energized molecules examples of intrinsic non-RRKM dynamics from experiments and simulations the role of anharmonidty in calculating accurate RRKM rate constants and quantum scattering and intrinsic RRKM and non-RRKM dynamics. 

Intrinsic non-RRKM dynamics occurs when transitions between individual molecular rovibrational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In terms of classical phase space dynamics, slow transitions between the states occur when the reactant phase space consists of several regions, which are weakly coupled on the timescale of the unimolecular reaction, and when there is at least one bottleneck in the phase space other than the one defining the TS. For non-exponential decay, one distinguishes an initial fast decay (faster than the RRKM rate) and a slower decay component which sets in at later times. The initial decay is faster than the RRKM prediction, because the reactive region of phase space is smaller than the total phase space for this initial decay. Thus the decomposing molecule behaves as a smaller molecule, a dynamical property first described by O. K. Rice in 1930. ... 

An extreme illustration of intrinsic non-RRKM dynamics occurs when one part of the phase space is totally decoupled from the reaction coordinate. The resulting relative N l) is ... 

A classical microcanonical ensemble for an intrinsie non-RRKM molecule consists of chaotic, vague tori and quasiperiodic trajeetories. Such a complex non-ergodie phase spaee strueture leads to a non-exponential P i). As an applieation of the KAM theorem, Oxtoby and Riee have shown that the intrinsic non-RRKM dynamics that Bunker found for model triatomic Hamiltonians results from insufficient internal resonances to yield ergodic dynamics. 

---